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[References: 52 tit.]

Identifying and characterizing natural fractures is essential for understanding fluid flow and drainage in many oil and gas reservoirs, particularly carbonate. The presence of fractures often enhances fluid recovery but substantially complicates reservoir flow performance. Information from cores and formation imaging logs is constrained by their availability and cost. Reliably predicting fracture density using petrophysical logs and machine learning (ML) is therefore a desirable objective for fields with reservoirs displaying intermittent and sparsely distributed fractures. In the first step, Hybrid ML-optimizer models are developed and applied to a large, high- resolution, dataset (10 petrophysical variables; 3395 data records; ∼12% of the records displaying fractures) from the Asmari fractured carbonate reservoir in Iran's Marun oil and gas field. Fracture density measured with a formation image log from one well is predicted by supervised learning using five hybrid models. The models use six of the ten petrophysical variables considered, based on feature selection, to predict fracture density.

The selected variables are: corrected gamma ray (CGR), neutron porosity (NPHI); compressional sonic transition time (DT); interpreted sonic porosity (PHIS); bulk formation density (RHOB); and, the photoelectric absorption factor (PEF). The models enhance the performance of distance-weighted K-nearest neighbor (DWKNN) and neural network (MLP) with firefly and artificial bee colony optimizers. The novel firefly-KNN model achieves higher fracture density prediction accuracy than the other models. It is further refined by executing it in two layers: the first layer detects fractures; the second layer predicts fracture density. The double-layer-firefly-KNN model (DL-FF-DWKNN) achieves excellent prediction accuracy of fracture density for the Asmari carbonate (Precision = 99%, Recall = 97%, and F1-score = 98%). This correlation-free data matching technique substantially outperforms the correlation-dependent neural network models evaluated for this dataset with sparsely distributed fractured zones. The generalizability of the developed algorithms is tested with datasets from two other Marun field wells achieving prediction results that confirm high accuracy in fracture detection and prediction of fracture density (FVDC).